arXiv:2507.21792v1 Announce Type: new Abstract: Bivariate causal direction identification is a fundamental and vital problem in the causal inference field. Among binary causal methods, most methods based on additive noise only use one single causal mechanism to construct a causal model. In the real world, observations are always collected in different environments with heterogeneous causal relationships. Therefore, on observation data, this paper proposes a Mixture Conditional Variational Causal Inference model (MCVCI) to infer heterogeneous causality. Specifically, according to the identifiability of the Hybrid Additive Noise Model (HANM), MCVCI combines the superior fitting capabilities of the Gaussian mixture model and the neural network and elegantly uses the likelihoods obtained from the probabilistic bounds of the mixture conditional variational auto-encoder as causal decision criteria. Moreover, we model the casual heterogeneity into cluster numbers and propose the Mixture Conditional Variational Causal Clustering (MCVCC) method, which can reveal causal mechanism expression. Compared with state-of-the-art methods, the comprehensive best performance demonstrates the effectiveness of the methods proposed in this paper on several simulated and real data.